$76$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $44$ less than $3$ times the number of away team fans. How many home team and away team fans attended the game?
Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 76}$ ${x = 3y-44}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${3y-44}$ for $x$ in the first equation. ${(3y-44)}{+ y = 76}$ Simplify and solve for $y$ $ 3y-44 + y = 76 $ $ 4y-44 = 76 $ $ 4y = 120 $ $ y = \dfrac{120}{4} $ ${y = 30}$ Now that you know ${y = 30}$ , plug it back into ${x = 3y-44}$ to find $x$ ${x = 3}{(30)}{ - 44}$ $x = 90 - 44$ ${x = 46}$ You can also plug ${y = 30}$ into ${x+y = 76}$ and get the same answer for $x$ ${x + }{(30)}{= 76}$ ${x = 46}$ There were $46$ home team fans and $30$ away team fans.